Real-Time Accelerometer Calibration

ABSTRACT

An electronic device configured for real-time calibration of an on-board accelerometer. A plurality of acceleration measurements are collected from the accelerometer to form a data set. An accelerometer error correction model is maintained that includes bias error calibration parameters, sensitivity calibration parameters, and cross-axis calibration parameters that each specify respective weights for each of bias error, sensitivity error, and cross-axis error. Calibration values are determined for one or more of the bias error calibration parameters, the sensitivity calibration parameters, and the cross-axis error calibration parameters for the data set of acceleration measurements using the accelerometer error correction model. A true acceleration vector may be determined that corresponds to a subsequently received acceleration measurement using the determined calibration values.

BACKGROUND

Field of Disclosure

The described embodiments relate to real-time calibration ofaccelerometers.

Description of the Related Art

An accelerometer measures the vector sum of forces from gravity andlinear acceleration, and in the absence of linear acceleration, theaccelerometer measures gravity alone. Since all accelerometers includesources of error (e.g., bias offset, sensitivity errors, cross-axiserrors and sensor noise errors), the measurements do not exactly matchthe vector sum of gravity and linear acceleration. This means that evenin the absence of linear acceleration, the estimate of the gravityvector likely includes errors directly caused by the sources of error inacceleration measurement.

To account for the sources of errors, accelerometers are typicallycalibrated during manufacturing. The calibration generally consists ofmanipulating the accelerometer (or a finished device including theaccelerometer) with high precision to known truth referenceorientations. However, maneuvering the accelerometer to known truthorientations adds both time and complexity to testing of devices, andaccordingly increases the manufacturing cost. In some cases,manufacturers may simply opt to skip accelerometer calibrationaltogether. Moreover, even if factory calibration occurs for anaccelerometer, that calibration is only accurate for a limited durationof time. For example, mechanical stresses, accelerometer age, andtemperature can all affect an accelerometer's calibration and thus theaccuracy of its measurements, and are not effectively accounted for byan initial factory calibration.

SUMMARY

An electronic device performs real-time calibration of an on-boardaccelerometer. A plurality of acceleration measurements are collectedfrom the accelerometer to form a data set. An accelerometer errorcorrection model includes calibration parameters that specify weights inthe form of calibration parameters for one or more of bias error,sensitivity error, and the cross-axis error in the presence of agravitational field. The error correction model and the accelerationmeasurements in the data set are used to determine calibration valuesfor bias error calibration parameters, sensitivity calibrationparameters, cross-axis error calibration parameters, or some combinationthereof. For example, calibration values for the bias error calibrationparameters may be determined, but not sensitivity calibration parametersor cross-axis error calibration parameters. The electronic device usesthe calibration values to, for example, calibrate accelerationmeasurements output from the accelerometer. Additionally, the electronicdevice may determine a calibration quality metric that quantitativelymeasures a quality of the calibration, and determine a true accelerationvector that corresponds to a subsequently received accelerationmeasurement using the determined calibration values and the errorcorrection model. In some embodiments, the electronic device providesthe calibration quality metric to one or more third party applicationsor devices along with one or more of the calibration values.

Over time certain conditions may cause the accelerometer to losecalibration. For example, mechanical stresses on a device package of theaccelerometer, may cause the accelerometer to lose calibration and thusoutput inaccurate measurements. The electronic device monitors one ormore recalibration conditions; if the recalibration conditions are metthe electronic device recalibrates the accelerometer by updating theaccelerometer error correction model. In this manner, the electronicdevice corrects for changes that would otherwise cause the accelerometerto fall out of calibration over time.

One embodiment of a method for real-time accelerometer calibration on anelectronic device, comprises collecting a plurality of accelerationmeasurements from an accelerometer to populate a data set, eachacceleration measurement representing an estimated acceleration vector,wherein each acceleration vector includes an error component thatoffsets the estimated acceleration vector from a true accelerationvector due to a combination of a bias error, a sensitivity error, and across-axis error. The electronic device maintains an accelerometer errorcorrection model that includes bias error calibration parameters thatspecify weights for the bias error of the estimated acceleration vectorcomponents. The electronic device determines calibration values for thebias error calibration parameters using the accelerometer errorcorrection model and the plurality of acceleration measurements. Theelectronic device determines a calibration corrected estimated of a trueacceleration vector that corresponds to a subsequently receivedacceleration measurement using the determined calibration values and theerror correction model.

Another embodiment of the method for real-time accelerometer calibrationon an electronic device, comprises collecting a plurality ofacceleration measurements from an accelerometer to populate a data set,each acceleration measurement representing an estimated accelerationvector, wherein each acceleration vector includes an error componentthat offsets the estimated acceleration vector from a true accelerationvector due to a combination of a bias error, a sensitivity error, and across-axis error. The electronic device maintains an accelerometer errorcorrection model that includes at least one set of calibrationparameters selected from a group consisting of: bias error calibrationparameters, sensitivity calibration parameters, and cross-axiscalibration parameters that each specify respective weights for each ofthe bias error, the sensitivity error, and the cross-axis error of theestimated acceleration vector components. The electronic devicedetermines calibration values for the at least one set of errorcalibration parameters determining values for the bias error calibrationparameters using the accelerometer error correction model and theplurality of acceleration measurements. The electronic device provides acalibration quality metric that is based in part on the calibrationvalues and one or more of the calibration values to a third partyapplication operating on the electronic device.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a block diagram illustrating an electronic device that isconfigured for real-time accelerometer calibration, according to anembodiment.

FIG. 1B is a plot of an estimated acceleration vector and itscorresponding true acceleration vector, according to an embodiment.

FIG. 2A is an example plot of orientation dependent tilt angle errorsdue to bias error.

FIG. 2B are example plots of magnitude of bias error (top trace) anderror in tilt angle estimate (bottom trace), based on a 100 millig biaserror on the z-axis.

FIG. 2C is an example plot of orientation dependent tilt angle errorsdue to sensitivity error, based on a z-axis sensitivity of 1.1 (10%high) and an x-axis sensitivity of 0.9 (10% low).

FIG. 2D are example plots of magnitude of acceleration error (top) anderror in tilt angle estimate (bottom), based on a sensitivity error of+0.1 on the z-axis and −0.1 in the x-axis.

FIG. 2E are example plots of magnitude of bias error (top trace) anderror in tilt angle estimate (bottom trace), based on an x axis to zaxis cross-axis error of 2%.

FIG. 2F are example plots of magnitude of bias error (top trace) anderror in tilt angle estimate (bottom trace), for accelerationmeasurements affected by the bias error, the sensitivity error, and thecross-axis error of FIGS. 2A-2E.

FIG. 3 is a block diagram illustrating a detailed view of modules withina calibration module according to one embodiment.

FIG. 4 is a flowchart illustrating a process of performing real-timeaccelerometer calibration according to one embodiment.

FIG. 5 is a flowchart illustrating a process of populating a data setaccording to one embodiment.

FIG. 6 is an example plot showing bias calibration convergence towardreference truth for x, y, and z axis.

FIG. 7 is an example plot showing sensitivity calibration convergencetoward reference truth for x, y, and z axis.

FIG. 8 is an example plot showing calibration convergence in terms oftilt angle

DETAILED DESCRIPTION

A calibration method for real-time calibration of an accelerometer onboard an electronic device is described herein. The calibration methoddoes not require comparing measurements against known truth referenceorientations (e.g., specific positions) as is typical in a factorycalibration. Instead the method calibrates the accelerometer inreal-time, and calibration may occur during normal operation and use aswell as at the factory.

An electronic device performing the calibration method collects aplurality of acceleration measurements from an accelerometer to populatea data set. The data set is populated in a manner to ensure that both(1) a minimum separation in angle (e.g., between 5 and 10 degrees)between each acceleration measurement in the data set, and (2) eachacceleration measurement has a linear acceleration component thatmaintained below a threshold value for at least a threshold period oftime. Each acceleration measurement represents an estimated accelerationvector, and each estimated acceleration vector includes error componentsthat cause the measured estimated acceleration vector to differ from thetrue acceleration vector.

The electronic device uses an accelerometer error correction model (alsoreferred to as an “error correction model”) to calibrate accelerationmeasurements. The error correction model specifies a weight for one ormore of various error sources (e.g., bias error, sensitivity error, andcross-axis error) in the presence of a gravitational field. Using theerror correction model and acceleration measurements in the data set,the electronic device identifies values for calibration parameters thatcharacterize the error sources.

In some embodiments, the electronic device determines a calibrationquality metric using the calibration values and the accelerationmeasurements in the data set, and provides the calibration qualitymetric, one or more of the calibration values, or some combinationthereof, to one or more third party applications (e.g., a fitnessapplication operating on the electronic device). In alternateembodiments, the electronic device updates a register on theaccelerometer with values of the calibration parameters, and theaccelerometer updates an on-board version of the error correction modelsuch that the accelerometer calibrates subsequent accelerationmeasurements to account for the error sources. For subsequently receivedacceleration measurements, the electronic device determinescorresponding true acceleration vectors using the determined values forthe bias error calibration parameters, the sensitivity calibrationparameters, and the cross-axis error calibration parameters. Thecalibration method monitors one or more recalibration conditions, thatif met, cause the electronic device to recalibrate the accelerometer.Thus, real-time calibration of the accelerometer during normal operationcan achieve higher long term accuracy than, for example, veryprecise—and potentially expensive—one-time factory calibrations.Further, because the calibration method uses data that is captured inreal time, the calibration method is able to account for conditions(e.g., age of the device, swings in temperature, etc.) that over timewould normally cause the accelerometer to lose calibration.

The Figures and the following description describe certain embodimentsof the calibration method and electronic device configured to performthe method, by way of illustration only. One skilled in the art willreadily recognize from the following description that alternativeembodiments of the structures and methods illustrated herein may beemployed without departing from the principles described herein.Reference will now be made in detail to several embodiments, examples ofwhich are illustrated in the accompanying figures. It is noted thatwherever practicable similar or like reference numbers may be used inthe figures and may indicate similar or like functionality.

FIG. 1A is a block diagram illustrating an electronic device 100 that isconfigured for real-time accelerometer calibration, according to anembodiment. The electronic device 100 is a computing device thatexecutes computer program modules which are stored on a non-transitorycomputer-readable medium and in turn use acceleration data provided byan accelerometer 110. The electronic device 100 may be, for example, asmartphone, a tablet computer, laptop computer, game controller, afitness device, navigation device, or included in a larger machine suchas an aircraft, a remotely operated vehicle, an autonomous vehicle, orany type of electronic device or machine that uses data from an onboardaccelerometer 110.

The electronic device 100 includes at least one processor 102 coupled toa chipset 104. The chipset 104 includes a memory controller hub 120 andan input/output (I/O) controller hub 122. A memory 106 and a graphicsadapter 112 are coupled to the memory controller hub 120, and a display111 is coupled to the graphics adapter 112. A storage device 108, aninput interface 114, the accelerometer 110, and a network adapter 116are coupled to the I/O controller hub 122. Other embodiments of theelectronic device 100 have different architectures.

The storage device 108 is a non-transitory computer-readable storagemedium such as a hard drive, compact disk read-only memory (CD-ROM),DVD, or a solid-state memory device. The memory 106 holds instructionsand data used by the processor 102. The input interface 114 is atouch-screen interface, a mouse, track ball, or other type of pointingdevice, a keyboard, or some combination thereof, and is used to inputdata into the electronic device 100. In some embodiments, the electronicdevice 100 may be configured to receive input (e.g., commands) from theinput interface 114 via gestures from the user. The graphics adapter 112displays images and other information on the display 111. The networkadapter 116 couples the electronic device 100 to one or more computernetworks. Additionally, the electronic device 100 may include one ormore temperature sensors 125. The one or more temperature sensors 125monitor the temperature of the accelerometer 110 and/or other componentsof the electronic device 100. The temperature sensors 125 may be, e.g.,a thermocouple or some other sensor that measures temperature. In someembodiments, the electronic device 100 can lack some of the componentsdescribed above, such display 111, graphics adapter 112, and temperaturesensor 125, and network adapter 116.

The electronic device 100 is adapted to execute computer program modulesfor providing functionality described herein. As used herein, the term“module” refers to computer program logic used to provide the specifiedfunctionality. Thus, a module can be implemented in hardware, firmware,and/or software. In one embodiment, program modules are stored on thestorage device 108, loaded into the memory 106, and executed by theprocessor 102.

The electronic device 100 further comprises an application 130 and acalibration module 135; the electronic device 100 may have differentmodules than those described here. Similarly, the functions can bedistributed among the modules in a different manner than is describedhere. For example, the calibration module 135 may be part of theaccelerometer 110 and/or the application 130.

The application 130 is any module that uses calibrated accelerationmeasurements to perform an action, and may be provided by a third party.The application 130 may be, for example, a program that uses thecalibrated acceleration measurements to track movement of the electronicdevice 100, a program that uses the calibrated acceleration measurementsto track an orientation (e.g., landscape, portrait, etc.) of theelectronic device 100, a navigation program that uses the accelerationmeasurements for dead reckoning, and some other software and/or hardwarethat uses the calibrated acceleration measurements. The application 130may include the error correction model, or some other relation that usesthe calibration values, to calibrate acceleration measurements such thatthey account for the error sources. The calibration relation uses one ormore calibration values provided by the calibration module 135 in orderto output calibrated acceleration measurements.

The accelerometer 110 measures acceleration forces, and outputs signals(e.g., voltage signal) that correspond to the measured accelerationforces as acceleration measurements. The accelerometer 110 may includeone or more single axis accelerometers, dual axis accelerometers, threeaxis accelerometers, or some combination thereof. For example theaccelerometer 110 may be a three axis accelerometer that measuresacceleration in three dimensions (x, y, and z). The accelerometer 110may include accelerometers of one or more types (e.g., surface or bulkmicromachined capacitive (MEMS), piezoelectric, thermal, strain gauge,etc.).

The accelerometer 110 outputs a signal that corresponds to a measuredacceleration force as an acceleration measurement. The accelerationmeasurement quantifies an estimated acceleration vector of theelectronic device 100. The acceleration measurement includes anx-component of an estimated acceleration vector, a y-component of theestimated acceleration vector, and a z-component of the estimatedacceleration vector in an x-y-z coordinate system. In other embodiments,the estimated acceleration vector may be described by other coordinatesystems (e.g., spherical). The acceleration measurements are preferablyin units of g's (e.g., 1 g=9.81 m/s²).

The estimated acceleration vector is comprised of a gravitationalcomponent, a linear acceleration component, an error component, or somecombination thereof. The gravitational component is representative ofthe Earth's gravitational force on the accelerometer 110. The linearacceleration component is representative of a force on the accelerometer110 other than the Earth's gravitational force. For example, in an idealcase (i.e., no error component) an accelerating accelerometer 110 wouldhave a linear acceleration component in the direction matching thenon-gravitational force applied and a gravitational component in thedirection of the Earth's gravity. The combination of the linearacceleration component and the gravitational component is a trueacceleration vector. The error component offsets the estimatedacceleration vector from the true acceleration vector due to one or moreerror sources. For example, FIG. 1B is a plot of an estimatedacceleration vector 150 and its corresponding true acceleration vector160, according to an embodiment. The estimated acceleration vector 150includes an x″ component, a y″ component, and a z″ component, and thetrue acceleration vector 160 includes an x′ component, a y′ component,and a z′ component. The offset between the vectors 150 and 160 is causedby one or more error sources. Turning back to FIG. 1A, an error sourcemay be, for example, a bias error, a sensitivity error, a cross-axiserror, or some combination thereof resulting from operational,environmental, or systematic features of the device 100 and itscomponents. The accelerometer 110 provides the acceleration measurementsto the calibration module 135.

The calibration module 135 collects acceleration measurements from theaccelerometer 110. As discussed below in detail with regard to FIGS. 3and 5, the calibration module 135 populates a data set in memory 106with the collected acceleration measurements (i.e., estimatedacceleration vectors). The calibration module 135 generates an errorcorrection model to model the relationship between error sources,estimated acceleration vectors, and true acceleration vectors; the errorcorrection model is also stored in memory 106. The generated errorcorrection model includes calibration parameters that describe biaserror, sensitivity error, cross-axis error, or some combination thereof.The calibration parameters are weights used by the model and figure ofmerit to describe the effects of error sources on true accelerationvectors. The calibration parameters are later described in detail belowfor each of the error sources.

The calibration module 135 uses the error correction model, accelerationmeasurements in the data set, and Earth's gravity to determinecalibration values for each of the calibration parameters. As discussedin detail below with regard to FIGS. 3 and 4, the calibration module 135perturbs, in a progressive and iterative manner, the calibrationparameters to generate various estimated acceleration measurements, andusing a modified variance of the estimated acceleration matricesdetermines values for each of the calibration parameters that result incorresponding minimum values of the modified variance. In someembodiments, once values of calibration parameters have been determinedto a particular precision (e.g., bit resolution or threshold deltavalue), the calibration module 135 calculates a calibration qualitymetric that quantifies a quality of calibration that may be achieved byusing the determined calibration values to correct for error inacceleration measurements output by the accelerometer 110. In someembodiments, the calibration module 135 provides the calibration qualitymetric, one or more of the calibration values, or some combinationthereof, to the application 130. In alternate embodiments, thecalibration module 135 updates a register on the accelerometer 110 withvalues of the calibration parameters, and the accelerometer 110 updatesan on-board version of the error correction model such that theaccelerometer 110 calibrates subsequent acceleration measurements toaccount for the error sources. The calibration module 135 then providesthe calibrated acceleration measurements via, e.g., an applicationperipheral interface, to the Application 130.

Bias error is the output of the accelerometer when the accelerometer 110is not experiencing any linear or gravitational force. For example,assuming the accelerometer 110 is on Earth and is not accelerating thetrue acceleration vector should be the gravitational component. However,if bias error is present, the accelerometer 110 would outputacceleration measurements that represent an estimated accelerationvector that is offset from the true acceleration vector. Bias error maybe described using a bias error calibration parameter for each of the x,y, and z, axis, (B_(x), B_(y), B_(z)), that collectively are referred toas bias error calibration parameters. Specific examples of bias errorare discussed below at FIGS. 2A and 2B.

Sensitivity error is associated with deviations from a specified asensitivity for an accelerometer 110. Sensitivity is a ratio in thechange in acceleration force (input) to a change in the estimatedacceleration vector (output), and is sometimes referred to as a “scalefactor” of an accelerometer. Ideally, the scale factor equals 1 for thex, y, and z axis, and is typically specified as being within a specifictolerance of the scale factor (e.g., scale factor ±0.02 for each axis)for a set of operating conditions specified by the manufacturer. Theoperating conditions may be, for example, a particular temperature range(e.g., 25° C.±5° C.), a particular acceleration amplitude (4 g, 8 g,etc.), a particular sampling frequency (e.g., 100 Hz), some othercondition that if varied affects the scale factor, or some combinationthereof. If the electronic device 100 operates outside of the specifiedoperating conditions, the scale factor may drift to different valuesoutside the specified tolerance. The deviation from the ideal value ofscale factor to some other value is the sensitivity error, and isdescribed using sensitivity calibration parameters for the x-axis(S_(x)), for the y-axis (S_(y)), and for the z-axis (S_(z)), thatcollectively are referred to as sensitivity calibration parameters,(S_(x), S_(y), S_(z)). In the ideal case the sensitivity calibrationparameters are (1, 1, 1), however, sensitivity error may be present forone or more axes. For example a sensitivity error of 10% along thex-axis, no error (ideal sensitivity) along y-axis and z-axis may berepresented by (1.1, 1, 1). Specific examples of sensitivity error arediscussed below at FIGS. 2C and 2D.

Cross-axis error is a measure of how much output is seen on one axiswhen acceleration is imposed on a different axis. Cross-axis error maybe caused by, e.g., fabrication error in beam positioning of a MEMSaccelerometer 110 or the accelerometer 110 being out of alignment withthe electronic device 100 it is mounted to. Given a true accelerationalong a specific axis (e.g., x-axis) cross-axis error causes theestimated acceleration vector to include acceleration along some otheraxis (e.g., y-axis or z-axis) in addition to the x-axis. Cross-axiserror may be described using a cross-axis error calibration parameterfor x to y axis (C_(x-y)), x to z axis (C_(x-z)), y to x axis (C_(y-x)),y to z axis (C_(y-z)), z to x axis (C_(z-x)), and z to y axis (C_(z-y)),that collectively are referred to as cross-axis error calibrationparameters, (C_(x-y), C_(x-z), C_(y-x), C_(y-z), C_(z-x), and C_(z-y)).Specific examples of cross-axis error are discussed below at FIG. 2E. Ofthe three error sources described herein, bias error tends to be thelargest, sensitivity error is typically but not always a smaller angleerror contributor than bias error, and cross-axis error is typically butnot always provides the smallest contribution to angle error.

Over time certain conditions may cause the accelerometer 110 errorparameters to change, causing previously measured calibration parametersto become less accurate. For example, mechanical stresses on a devicepackage of the accelerometer 110, aging of the accelerometer 110, andtemperature changes, all may cause the accelerometer 110 calibration todegrade. The calibration module 135 monitors one or more recalibrationconditions that if met, cause the calibration module 135 to recalibratethe accelerometer 110. In this manner, the calibration module 135corrects for changes that would otherwise cause the accelerometer 110 tofall out of calibration over time. For example, the calibration module135 monitors the output of the temperature sensor, and if thetemperature deviates more than a threshold value from a temperature atwhich the previous calibration as performed (i.e., meets a recalibrationcondition), the calibration module 135 re-calibrates the accelerometer110. Accordingly, real-time calibration of the accelerometer duringnormal operation can achieve higher long term accuracy than factorycalibration since the calibration parameters can be updated in real-timewhen needed.

FIGS. 2A-2F illustrate the types of error sources that may be present inan acceleration measurement. The curves represented in FIGS. 2A-2F arenot used by the electronic device 100 to calibrate the accelerometer,and are included merely to help explain the different forms of error.

FIG. 2A is an example plot 200 of orientation dependent tilt angleerrors due to bias error. The plot 200 is based on a 100 millig biaserror on the z-axis, and for simplicity, does not show bias error on thex-axis and y-axis. In practice, bias error may also occur along thex-axis and the y-axis. The plot 200 shows true acceleration vectors202A, 204A, 206A, 208A, and 210A that represent true acceleration in anideal case where all error sources are zero. Additionally, the plot 200shows the measured acceleration vectors when a 100 millig bias ispresent as 202B, 204B, 206B, 208B, and 210B. In FIG. 2A, an estimatedacceleration vector is the true acceleration vector offset by biaserror. Notice that when the acceleration vectors are parallel to thez-axis, e.g., accelerating straight up (e.g., vectors 202A, 202B) orstraight down (e.g., vectors 210A, 210B) the tilt angle error is zero.Where the actual and estimated acceleration vectors deviate from thez-axis there is error in tilt angle that manifests as offset between theactual and estimated acceleration vectors, specifically offset 212between vectors 204A and 204B, offset 214 between vectors 206A and 206B,and offset 216 between vectors 208A and 208B.

FIG. 2B are example plots 220 of magnitude of bias error (top trace) anderror in tilt angle estimate (bottom trace), based on a 100 millig biaserror on the z-axis. With reference to FIG. 2A, the vector at 206A is atzero degrees rotation, and the vector 202A is at 90 degrees rotation.The difference in magnitude of vectors 206A and 206 B is close tozero—which matches the magnitude of bias error for 0 degrees rotation inthe top trace. Similarly, it is apparent from FIG. 2A that there is anangular offset 214 between vectors 206A and 206B, from the bottom traceshows for zero degrees rotation value of ˜5.8 degrees—which is the angleof the offset 214.

FIG. 2C is an example plot 230 of orientation dependent tilt angleerrors due to sensitivity error. The plot 230 is based on a sensitivityerror on the z-axis where sensitivity is 1.1 times an ideal sensitivity(i.e., 1), and where sensitivity on the x-axis is 0.9 times an idealsensitivity (i.e., 1). In practice, sensitivity error may also occuralong any and all axes. The plot 230 shows true acceleration vectors232A, 234A, 236A, 238A, and 240A. The true acceleration vector is anideal case where all error sources are zero. Additionally, the plot 230shows estimated acceleration vectors 232B, 234B, 236B, 238B, and 240B.In FIG. 2C, an estimated acceleration vector is the true accelerationvector scaled by a non-unity sensitivity value. Like in FIG. 2A, whenaccelerating along the z-axis (e.g., vectors 232A and 232B, and vectors230A and 230B) the tilt angle error is zero—basically cases where thevectors align with or against the Earth's gravity, however, for caseswhere the actual and estimated acceleration vectors deviate from thez-axis there is error in tilt angle that manifests as an offset betweenthe actual and estimated acceleration vectors. Where the actual andestimated acceleration vectors deviate from the z-axis there is error intilt angle that manifests as offset between the actual and estimatedacceleration vectors, specifically offset 242 between vectors 234A and234B, and offset 244 between vectors 238A and 238B.

FIG. 2D are example plots 250 of magnitude of acceleration error (top)and error in tilt angle estimate (bottom), based on a sensitivity errorof +0.1 on the z-axis and −0.1 on the x-axis. With reference to FIG. 2C,the vector at 236A is at zero degrees rotation, and the vector 232A isat 90 degrees rotation Similarly, it is apparent from FIG. 2C that thereis zero angular offset between vectors 236A and 236B, this matches thezero angular offset shown in the bottom trace for a rotation angle ofzero degrees.

Cross-axis error is generally much lower than bias error and sensitivityerror, however, for completeness, FIG. 2E are example plots 260 ofmagnitude of bias error (top trace) and error in tilt angle estimate(bottom trace), based on an x-axis to z-axis cross-axis error of 2%. Forsimplicity FIG. 2E, does not illustrate cross-axis error on, e.g., thex-axis to the y-axis, the z-axis to the axis, etc., which in practicemay be present. In the ideal case, cross-axis error would be zero.However, for the data presented in plot 260 there is cross-axis errorpresent, however, it is small relative to the bias error and sensitivityerror presented above in FIGS. 2A-2D. For example, in plot 260 the errorin magnitude is between AO millig, and the error is always less than˜1.3 degrees. In contrast, plot 220 indicates that for bias error, theerror in magnitude is between ±100 millig, and the error is always lessthan ˜5.8 degrees, and plot 250 indicates that for sensitivity error,the error in magnitude is between ±100 millig, and the error rangesbetween ±5.2 degrees.

While FIGS. 2A-2E show individual errors, it is useful to see how theseerrors combine. FIG. 2F are example plots 270 of magnitude of bias error(top trace) and error in tilt angle estimate (bottom trace), foracceleration measurements affected by the bias error, the sensitivityerror, and the cross-axis error of FIGS. 2A-2E. Note that the bias errorof up to 100 millig, a sensitivity error of +/−10%, and a cross-axiserror of 2% are typical of many modern consumer grade accelerometers.FIG. 2F clearly shows that these error sources can results in ratherlarge errors, specifically, a maximum error in magnitude of ˜200 milligat a 90 degree rotation angle, a maximum error in angle of ˜11 degreesat a rotation angle of ˜28 degrees.

Turning now to a discussion of the structure of the calibration module135, FIG. 3 is a block diagram illustrating a detailed view of moduleswithin the calibration module 135 according to one embodiment. Someembodiments of the calibration module 135 have different modules thanthose described here. Similarly, the functions can be distributed amongthe modules in a different manner than is described here. Thecalibration module 135 is comprised of modules including anaccelerometer data store 410, a data collection module 320, a modelingmodule 330, an error module 340, an application interface module 350,and a monitoring module 360.

The accelerometer data store 310 stores information relating to theaccelerometer 110 and its calibration. Information relating to theaccelerometer 110 includes acceleration measurements output from theaccelerometer 110, default values for calibration parameters for errorsources, calibrated values for error source calibration parameters, oneor more temperatures associated with a calibration of the accelerometer110, or some combination thereof. Acceleration measurements are outputfrom the accelerometer 110. Each acceleration measurement representingan estimated acceleration vector that includes an error component thatoffsets the estimated acceleration vector from a true accelerationvector. The offset is due to bias error, sensitivity error, cross-axiserror, or some combination thereof.

The data collection module 320 collects acceleration measurements fromthe accelerometer 110 to populate a data set of size N (e.g., 128samples of acceleration measurements). The data collection module 320 iscoupled to receive the acceleration measurements in the x, y, and z axesas they are output from the accelerometer 110. While the data set is notfull (i.e., less than N samples have been collected), the datacollection module 320 populates the data set in accordance with aplurality of population conditions. The population conditions controlwhether or not the data collection module 320 adds a receivedacceleration measurement to the data set. The population conditionsinclude a maximum linear acceleration (e.g., between ±50 millig) withina specified period of time (e.g., 100 ms) and a minimum threshold angle(e.g., 7.5 degrees) between the received acceleration measurement andany of the acceleration measurements already present in the data set. Inalternate embodiments, the population conditions may additionallyinclude, some other property of an acceleration measurement, the numberof acceleration measurements in the data set, or some combinationthereof.

Upon initiation of the calibration process, if the data set is empty,once a new acceleration measurement is received, the data collectionmodule 320 determines whether the population conditions are met. Asnoted above, one population condition is that (1) a linear accelerationcomponent of the new acceleration measurement is below a maximum linearacceleration, and (2) that the linear acceleration component has beenbelow the maximum linear acceleration for a specified period of time(e.g., 100 ms). The data collection module 320 compares the linearacceleration component of the new acceleration measurement to themaximum linear acceleration. The data collection module 320 alsodetermines how long the linear acceleration component is within amaximum allowed value (e.g., between ±50 millig) by comparing the linearacceleration component of the new acceleration measurement to linearacceleration components determined from one or more previously receivedacceleration measurements. If both (1) and (2) are met, this populationcondition is satisfied.

Another population condition is whether the new acceleration measurementis outside of a minimum threshold angle with the accelerationmeasurements in the data set. In some embodiments, to determine whethera subsequent acceleration measurement, AM_(new), is outside of athreshold angle with other acceleration measurements in the data set(e.g., AM_(i)), the data collection module 320 determines a set ofangles (θ₁, θ₂, . . . θ_(N)) between AM_(new) and each of the previouslystored acceleration measurements AM_(i), using a relation derived fromthe dot product of two acceleration measurements:

$\begin{matrix}{\theta_{i} = {\cos^{- 1}\left( \frac{{AM}_{new} \cdot {AM}_{i}}{{{AM}_{new}{{Am}_{i}}}} \right)}} & (1)\end{matrix}$

where AM_(i) is the acceleration measurement in the i^(th) position ofthe data set, and i is an integer than ranges between 1 and N, and θ_(i)is the corresponding angle between AM_(new) and AM_(i). In this manner,the data collection module 320 uses equation (1) to determine the set ofangles between AM_(new) and each of the acceleration measurements in thedata set. The data collection module 320 compares the set of angles tothe minimum angle threshold, and if each angle in the set of angles isgreater than the minimum angle threshold, the population condition issatisfied. The evaluation of each new measurement against all previousmeasurements is simple, but may not be the most efficient, especially asthe data set increases in size. In other embodiments, the datacollection module 320 may use other, possibly more efficient, but morecomplex algorithms to populate the data set. For example, the datacollection module 320 may use a binary search algorithm, a nearestneighbor algorithm, or some other algorithm to populate the data setwith acceleration measurements that are separated by at least thethreshold angle value from adjacent acceleration measurements.

The threshold angle value is chosen such that there is a minimum angle(e.g., a value between 5 and 10 degrees, e.g. 7.5 degrees) between eachof the estimated acceleration vectors that are described by theircorresponding acceleration measurement. Accordingly, accelerationmeasurements in the data set have a minimum separation in angle.Conceptually, each estimated acceleration vector points at some point ona surface of an ellipsoid. The data set includes accelerationmeasurements that are each unique (not a duplicate accelerationmeasurement) and are separated from other acceleration measurements bythe threshold angle value. The corresponding estimated accelerationvectors point to different points across the entire ellipsoid, in arelatively uniform manner. This results in a better calibration that isless susceptible to noise than, for example, cases where the data setonly includes acceleration measurements that cover only the same orclose to the same portion of the ellipsoid. In practice, a reasonablenumber of data samples in the data set is 128. Assuming the ellipsoid isa sphere, if directional coverage is uniform over the sphere, with thisnumber of acceleration measurements, each estimated acceleration vectoris angled approximately 20 degrees from other adjacent estimatedacceleration vectors. If the acceleration measurements collected aresuch that the sphere is totally uniformly sampled, fewer data points maybe used, however, 128 has been found to offer sufficient coverage thatmakes large coverage gaps unlikely while remaining computationallyinexpensive.

In some embodiments, the data collection module 320 may modify one ormore of the population conditions. The data collection module 320 may,for example, reduce the maximum linear acceleration, adjust thespecified period of time associated with the maximum linearacceleration, adjust the minimum threshold angle, or some combinationthereof to reduce computational load, calibration time, or increase ordecrease calibration accuracy. The data collection module 320 may adjustone or more of the population conditions responsive to instructions fromthe error module 340.

Initially populating the data set in accordance with the populationconditions facilitates the collected measurement having sufficientcoverage over a full range of possible acceleration measurements. Due tothe population conditions, it may take, for example, many hundreds ofacceleration measurements to occur before the data set is completelyfiled. For example, it may take approximately 1,000 accelerationmeasurements to be received, before a data set of size N=128 iscompletely filed. In order to have sufficient number of measurements toreach a calibration solution the collected data set of accelerationmeasurements is greater than or equal to the number of unknowncalibration parameters. In practice, as real-time calibration of theaccelerometer 110 occurs in the field and not at the factory with truthreferences, the collected set of acceleration measurements is muchlarger than the number of unknown calibration parameters. The size(i.e., N) of the data set may be, for example, 128, 256, or some othernumber larger than the total number of calibration parameters.

The data collection module 320 continues to collect accelerationmeasurements even though the data set is full. As discussed below withregard to FIG. 5, the data collection module 320 identifies any extremumin the data set. An extremum is an acceleration measurement that, oncecalibrated, has a maximum magnitude (Max) above a maximum thresholdvalue or a minimum magnitude (Min) that is below a minimum thresholdvalue. In cases where an extremum is present in the data set, the datacollection module 320 compares a magnitude of a calibrated value of thenew acceleration measurement to the magnitude associated with theextremum. If the calculated magnitude is closer to an expected value(e.g., 1 g) than the Max or Min values the data collection module 320replaces the acceleration measurement associated with the extremum withthe new acceleration measurement, otherwise the data collection module320 discards the new acceleration measurement.

In embodiments, where no extremum is present in the data set, the datacollection module 320 identifies the two acceleration measurements thatare closest in angle among the acceleration measurements in the data setand the new acceleration measurement. In some embodiments, the datacollection module 320 uses a dot product based algorithm (e.g., as inequation (1)) to determine an angle between acceleration measurements inthe data set and between acceleration measurements in the data set and anew acceleration measurement. The data collection module 320 may use abrute force exhaustive search, a binary search algorithm, a nearestneighbor algorithm, or some other algorithm to determine the two closestacceleration measurements that are closest in angle.

The data collection module 320 then combines the two closestacceleration measurements to generate a combined accelerationmeasurement. The electronic device 100 combines the two closestacceleration measurements using a weighted sum to generate a combinedacceleration measurement. In the simplest case, the weights are equal,and the combined acceleration measurement is a linear interpolationbetween the two acceleration measurements. Alternatively, the electronicdevice 100 may be configured to weight each of the closest accelerationmeasurements based on a respective number of acceleration measurementsthat were previously combined to generate each of the two closestacceleration measurements. In this approach, for each location in thedata set, the data collection module 320 maintains a count ‘m’ of thenumber of acceleration measurements that were combined to generate theacceleration measurement that occupies each location in the data set,along with the current value AM_(i) of the vector at that location. Forexample, assuming one of the two closest acceleration measurements isthe new acceleration measurement, AM_(new), and the other of the twoclosest acceleration measurements is AM_(i) the data collection module320 combines the vectors AM_(i) and AM_(new) as((m*AM_(i))/(m+1)+AM_(new)/(m+1)). For example, if four accelerationmeasurements had contributed to an existing combined accelerationmeasurement in position 1, AM₁, and the data collection module 320 isconfigured to combine it with another acceleration measurement,AM_(new), the new acceleration measurement can be a linear interpolationweighted 80% by the weight of AM₁, and 20% by the weight of AM_(new).This is very close to the geometric centroid of all of four accelerationmeasurements previously combined to generate AM₁. The combinedacceleration measurement is then placed in the position of the data setformerly occupied by AM₁. In embodiments, where the two closestacceleration measurements are both within the data set, the datacollection module 320 combines the two acceleration measurement in asimilar manner as described above, but now replaces one of the twoacceleration measurements with the combined acceleration measurement andreplaces the other of the two acceleration measurements with the newacceleration measurement.

By preferentially combining close acceleration measurements and directlyincluding acceleration measurements that improve coverage, the angularcoverage of the measurements in the data set gradually becomes moreuniform. Additionally, as the number of acceleration measurements thatcontribute to each combined acceleration measurement increases, theeffect of noise and linear acceleration is further reduced.

The data collection module 320 determines that a threshold number ofacceleration measurements are in a data set and pass the data set toanother module, while additional acceleration measurements are beingreceived. For example, once a threshold number of accelerationmeasurements less than N are in the data set (e.g., 0.75 N), the datacollection module 320 passes the acceleration measurements in the dataset to another module which can use the acceleration measurements, whileadditional measurements are being received. In this manner the data setdoes not have to be entirely populated with N acceleration measurementsbefore other modules may use the data. Alternatively, in someembodiments, the data collection module 320 populates the entire dataset before passing it on to other modules.

The modeling module 330 maintains an accelerometer error correctionmodel that models the effects of the error sources on actual linearacceleration and gravitational components using an accelerometer errorcorrection model (“error correction model”). The error correction modelspecifies a weight for each of the bias error, the sensitivity error,and the cross-axis error in the presence of a gravitational field. Themodeling module 330 uses the error correction model to model the effectsof bias error, sensitivity error, and cross-axis error on accelerationmeasurements. An embodiment of an error correction model that neglectssensor noise is:

â=S(a−b)  (2)

where vector a are the acceleration measurements (i.e., uncalibrateddata), b is the vector for bias error including bias error calibrationparameters, S is a matrix including sensitivity calibration parameterson the matrix diagonals and cross-axis calibration parameters occupyingthe non-diagonal terms, and â is the estimated acceleration measurement.Accordingly, given a set of calibration values for the calibrationparameters, and an acceleration measurement, equation (2) outputs anestimated acceleration measurement—which ideally would match the trueacceleration.

The error module 340 determines values for the calibration parametersusing the error correction model and the data set. In some embodiments,the electronic device 100 may then use a process similar to that ofdescribed below in FIG. 4, but on 3, 6, or 9 parameters instead of 12.For example, the error module 340 may determine values for the biaserror calibration parameters, the sensitivity calibration parameters,the cross-axis error calibration parameters, or some combinationthereof. Another simplification assumes that the sensitivity matrix isthe identity matrix. The lower parameter number calibrations typicallyremove most of the error associated with the accelerometer 110, but maynot provide calibrated measurements that fit as well as the full 12parameter case described below with reference to FIG. 4. One advantageto calculating a lower number (i.e., less than 12) of calibration valuesis that it uses less computation than calculating calibration values forthe bias error calibration parameters, the sensitivity calibrationparameters, and the cross-axis error calibration parameters.Accordingly, calculating the lower number of calibration values mayreduce processor load, memory load, power consumption, etc. on theelectronic device 100.

The error module 340 initially sets each of the calibration parametersin the error correction model to their respective default values. Thedefault values are set to a value of ‘1’ for sensitivity calibrationparameters, and to a value of ‘0’ for bias error and cross-axiscalibration parameters—which correspond to the case of no error sources.Alternatively, the default values may be set to some other values (e.g.,values associated with typical error values for each error source, orvalues stored to the accelerometer data store 310 from a previous orfactory calibration).

The error module 340 minimizes the error correction model by iterativelyperturbing, in a graduated manner, each of the calibration parameters.In some embodiments, these iterative perturbations of the calibrationparameters are applied continuously as long as new accelerometer datasamples are acquired. In other embodiments, the perturbations arestopped when the error module 340 observes that the calibrationparameters have converged such that calibration parameter updates havebecome progressively smaller and have dropped below a set of thresholdvalues. As described below, the error module 340 first determines valuesfor the bias error calibration parameters. The error module 340 thendetermines values for the sensitivity calibration parameters whilerefining the previously determined values for the bias error calibrationparameters. The error module 340 then determines values for the crossaxis error calibration parameters and finalizes the values for the biaserror and sensitivity calibration parameters. In this manner, a roughapproximation of values for the bias error calibration parameters aresolved for first—which is generally the largest error source—and shouldhelp increase the speed at which the values for the remainingcalibration parameters and the final values for the bias errorcalibration error are determined.

An in depth discussion of how each of the calibration parameters isdetermined is discussed below with reference to FIG. 4. The error module340 is configured to determine values for the bias error calibrationparameters using the accelerometer error correction model and theplurality of acceleration measurements. In brief, the error module 340first determines values for the bias error calibration parameters usingthe error correction model and the data set. The error module 340selects a particular bias error calibration parameter (e.g., Bx) andfixes the remaining calibration parameters. The error module 340perturbs the selected bias error calibration parameter by a value of A.Specifically, the error module 340 selects 3 separate values for theselected calibration parameter which correspond to a most recent value(MRV₀), a most recent value −Δ (MRV_(−Δ)), and a most recent value +Δ(MRV_(+Δ)), where A is constant value at a first resolution (e.g., 0.1millig). The error module 340 determines an estimated accelerationvector for each of the acceleration measurements in the data set using aMRV_(−Δ) of the particular bias error calibration parameter, a MRV₀ ofthe particular bias error calibration parameter, and a MRV_(+Δ) of theparticular bias error calibration parameter, respectively, to generatethree estimated acceleration matrices. The error module 340 determines amodified variance of each of the estimated acceleration matrices. Forexample, a modified variance, σ, of an estimated acceleration matrix maybe found via:

σ=Σ_(i=1) ^(n) [x _(i) ² +y _(i) ² +z _(i) ² −E] ²  (3)

Where x is the x component at row i in the estimated accelerationmatrix, y is the y component at row i in the estimated accelerationmatrix, z is the z component at row i in the estimated accelerationmatrix, and E is the expected value which is 1 g. Note, in someembodiments, the sum of x_(i) ²+y_(i) ²+z_(i) ² in equation (3) may bereplaced with √{square root over (x_(i) ²+y_(i) ²+z_(i) ²)}. The errormodule 340 selects the value of the bias error calibration parameterthat results in the lowest modified variance, and sets the selectedvalue as a new MRV₀. The error module 340 then selects new values forMRV_(+Δ) and MRV_(+Δ). based on the value of the new MRV₀. The errormodule 340 then calculates the acceleration matrices, calculatesmodified variances of each estimated acceleration matrix, and identifieswhich of the MRV_(−Δ), MRV₀, or MRV_(+Δ), results in the lowest modifiedvariance.

This iterative process of adjusting the MRV₀ of the selected bias errorcalibration parameter continues until the MRV₀ (and not the MRV_(−Δ) orthe MRV_(+Δ)) for the particular bias error calibration parameterresults in a corresponding minimum modified variance value. The errormodule 340 then reduces the value of A by X % (e.g., 50% or some othervalue). The error module 340 repeats the above described iteration forthe particular bias error calibration parameter (e.g., Bx) using the newvalue of A until the MRV₀ for the particular bias error calibrationparameter results in the minimum modified variance value, and not theMRV_(−Δ) or the MRV_(+Δ). The value of A may be reduced again, and theabove process repeated in a progressive manner, until the lowestcalculated modified variance value of the estimated accelerationmatrices is less than or equal to a bias error calibration threshold(e.g., 0.1 millig). The bias error calibration threshold determines howprecise a value is determined for a bias error calibration parameter.The bias error calibration threshold may be, e.g., a number set by anadministrator, or a number set by the bit resolution of the electronicdevice 100. An intermediate value is a value of a calibration parameterthat results in a lowest modified variance of an acceleration matrix fora given iteration. Once the bias error calibration threshold is reached,the electronic device 100 sets the particular bias error calibrationparameter (e.g., Bx) as the intermediate value.

The error module 340 then updates the perturbed calibration parameter(Bx) with the selected value, and selects a different bias errorcalibration parameter (e.g., By or Bz) for perturbation, and repeats theabove process for the newly selected calibration parameter, and so on.In this manner, the error module 340 cycles through each of the biaserror calibration parameters until, for all three calibrationparameters, the most recent values (MRV₀) of the calibration parametersresult in minimum modified variance values that are less than or equalto the bias error calibration threshold.

Conceptually, the modified variance values (V) are such that there arethree possible configurations: (1) increasing (e.g., V_(Δ−)<V₀<V_(Δ+));a (2) decreasing (e.g., V_(Δ−)>V₀>V_(Δ+)); or (3) minimum (e.g.,V_(Δ−)>V₀<V_(Δ+)). Essentially, the iterative perturbation describedabove, determines values of the bias error calibration parameters thatresult in a minimum configuration, reduces Δ, and again determinesvalues of the bias error calibration parameters that result in a minimumconfiguration, and so on. In this manner an initial values of the biaserror calibration parameters are found. Additionally, as error module340 continues to refine the initial values of the bias error calibrationparameters, as described below, during the determination of the valuesfor the sensitivity calibration parameters and the cross-axis errorcalibration parameters.

The error module 340 is configured to determine values for sensitivitycalibration parameters that specify weight for the sensitivity error,and refine the determined values for the bias error calibrationparameters using the accelerometer error correction model and theplurality of acceleration measurements. The error module 340 determinesvalues for the sensitivity calibration parameters and refines the valuesfor the bias error calibration in a manner similar to that describedabove for determining values for the bias error calibration parameters.The difference being that now the three sensitivity calibrationparameters are perturbed as well as the three bias error calibrationparameters. Additionally, the sensitivity calibration parameters areperturbed by γ, and γ is constant value at a first resolution (e.g.,0.01) and may be different from Δ. The error module 340 iterativelyperturbs the sensitivity calibration parameters and the bias errorcalibration parameters until (1) for all the sensitivity calibrationparameters the most recent values (MRV₀) of the sensitivity calibrationparameters result in minimum modified variance values that are less thanor equal to a sensitivity error calibration threshold, and (2) the mostrecent values (MRV₀) of all of the bias error calibration parametersresult in minimum modified variance values that are less than or equalto the bias error calibration threshold. The sensitivity calibrationthreshold determines how precise a value is determined for a sensitivitycalibration parameter. The sensitivity error calibration threshold maybe, e.g., a number set by an administrator, or a number set by the bitresolution of the electronic device 100.

The error module 340 is configured to determine calibration values forthe cross-axis error calibration parameters, and refine the determinedvalues of the sensitivity calibration parameters and the bias errorcalibration parameters using the error correction model and theplurality of acceleration measurements. The error module 340 determinesvalues for the cross-axis error calibration parameters and refines thevalues for the bias error calibration parameters and sensitivitycalibration parameters in a manner similar to that described above,except each of the 12 calibration are perturbed. For example, the errormodule 340 sequentially perturbs the 6 cross axis error calibrationparameters, the 3 sensitivity calibration parameters, and the 3 biaserror calibration parameters.

The values of the cross-axis error calibration parameters are perturbedby Γ, the sensitivity calibration parameters are perturbed by γ, and thebias error calibration parameters are perturbed by Δ, and Γ is constantvalue at a first resolution and may be different from Δ and/or γ. Theerror module 340 iteratively perturbs, in a graduated manner (i.e.,progressively reducing the size of Δ, γ, and/or Γ) each of thecalibration parameters until (1) the most recent values (MRV₀) of eachof the cross-axis error calibration parameters result in minimummodified variance values that are less than or equal to a cross-axiserror calibration threshold; (2) the most recent values (MRV₀) of eachof the sensitivity calibration parameters result in minimum modifiedvariance values that are less than or equal to the sensitivity errorcalibration threshold; and (3) the most recent values (MRV₀) of each ofthe bias error calibration parameters result in minimum modifiedvariance values that are less than or equal to the bias errorcalibration threshold. The values of the calibration parameters once(1), (2), and (3) are met are referred to as calibration values for thecalibration parameters. The cross-axis error calibration thresholddetermines how precise a value is determined for a cross-axis errorcalibration parameter. The cross-axis error calibration threshold maybe, e.g., a number set by an administrator, or a number set by the bitresolution of the electronic device 100.

The error correction module 320 determines a calibration quality metric(“C”) using the determined calibration values. The calibration qualitymetric may be used by the application 110, and/or the electronic device100 to make a quantitative assessment of the quality of the calibrationof the acceleration measurements. The calibration quality metric is afigure of merit that combines how well the data points cover the sphere(e.g., via m₁) with how small the standard deviation of the magnitude isfrom the expected value of Earth's gravity (e.g., via m₂). For example:

$\begin{matrix}{C = {m_{1}*m_{2}{\mspace{11mu} \;}{where}}} & (4) \\{m_{1} = \frac{\left( {x_{\max} - x_{\max}} \right)*\left( {y_{\max} - y_{\min}} \right)*\left( {z_{\max} - z_{\min}} \right)}{\left( {2*{Gravity}_{Earth}} \right)^{3}}} & (5) \\{m_{2} = {\log_{2}\left( \frac{1}{variance} \right)}} & (6)\end{matrix}$

and x_(max), y_(max), and z_(max) are, respectively, the maximum x, y,and z components of the calibrated acceleration matrix in g, x_(min),y_(min), and z_(min) are, respectively, the minimum x, y, and zcomponents of the calibrated acceleration matrix in g, andGravity_(Earth) is Earth's gravity in g (i.e., 1 g), and

$\begin{matrix}{{Variance} = \frac{\sum\limits_{i = 1}^{n}\left\lbrack {{ax}_{i}^{2} + {ay}_{i}^{2} + {az}_{i}^{2} - {Gravity}_{Earth}} \right\rbrack^{2}}{n}} & (7)\end{matrix}$

where ax is the x component at row i in the calibrated accelerationmatrix, ay is the y component at row i in the calibrated accelerationmatrix, az is the z component at row i in the calibrated accelerationmatrix, and n is the number of acceleration measurements in the dataset. Note, in some embodiments, the sum of ax_(i) ²+ay_(i) ²+az_(i) ² inequation (7) may be replaced with

√{square root over (ax _(i) ^(2+ay) _(i) ² az _(i) ²)}.  (8)

m₁ generally represents how well the calibrated accelerationmeasurements in the data set cover a uniform sphere with a 1 g radius.The error correction module 320 identifies a minimum and a maximum valueof the x, y, and z components within the calibrated acceleration matrix.In the ideal case the min and max values for x, y, and z, would be 1 gand −1 g, in practice the values are likely very close to 1 g or −1 g.Additionally, with regard to m₂, in this embodiment, the log₂ of theinverse of the Variance is used because it results in a monotonicallyincreasing function, that gives a higher value as the variance getssmaller.

Accordingly, C is some scalar number along a range of numbers. In someembodiments, the range of numbers is partitioned into different segmentsthat each correspond to different levels of quality. For example, lowquality, good quality, and excellent quality may correspond to,respectively, greater than 5% error between actual accelerationmeasurements and the calibrated acceleration measurements, between 5%and 1% error between actual acceleration measurements and the calibratedacceleration measurements, and less than 1% error between actualacceleration measurements and the calibrated acceleration measurements.Continuing with the above example, C values from 0 to 1000 maycorrespond to low quality calibration, from 1001 to 4000 may correspondto good calibration quality metric, and greater than 4000 may correspondto excellent calibration quality metric. Accordingly, the C value mayprovide a simple metric that evaluates the quality of the calibrationwhich may be achieved using the calibration values and the errorcorrection model.

The application interface module 350 is configured to determine a trueacceleration vector that corresponds to a subsequently receivedacceleration measurement using the determined calibration values and theerror correction model. For example, the application interface module350 may use equation (2) and the calibration values to calibrate thesubsequently received acceleration measurement.

In some embodiments, the application interface module 350 provides 440the calibration quality metric and/or one or more the calibration valuesto the application 110. Using the calibration values and equation (2),the application interface module 350 is able to solve for an estimatedacceleration measurement a given an acceleration measurement a. In someembodiments, the application interface module 350 provides some, but notall of the calibration values to the application 110. For example, theapplication interface module 350 may provide the calibration values forthe bias error and sensitivity calibration parameters, but not the crossterm error calibration parameters. In alternate embodiments, theapplication interface module 350 may provide one or more of thecalibration values, but not the calibration quality metric. Also, inalternate embodiments, the application interface module 350 may providethe error correction model and/or one or more of the calibration valuesto the application 110. In some embodiments the application interfacemodule 350 updates a register on the accelerometer 110 with values ofthe calibration parameters, which then updates an on-board version ofand/or equation (2) with the determined values for the calibrationparameters.

The monitoring module 360 monitors one or more recalibration conditions.A recalibration condition is a condition that if met, causes theelectronic device 100 to re-calibrate the accelerometer 110. Arecalibration condition may be, e.g., a change in temperature of theelectronic device 100 beyond a range of temperatures that relative to atemperature of the electronic device 100 during a previous calibration,an elapsed time since the previous calibration of the accelerometer(e.g., more than a week), a number of power cycles (e.g., more than 1),a user input (e.g., user manually requests re-calibration of theaccelerometer 110), some other condition, or some combination thereof.The monitoring module 360 monitors the one or more recalibrationconditions, and if a recalibration condition is met causes theelectronic device 100 to re-calibrate the accelerometer 110.

For example, once the calibrated values of the calibration parametersare determined, the monitoring module 360 may associate a calibrationtemperature with the set of calibration values. The calibrationtemperature is the temperature at which the calibrated values weredetermined as is determined using temperature measurements received fromthe temperature sensor 125. The calibration temperature may be, e.g., anaverage temperature of the accelerometer 110 while the calibrated valueswere determined, or some temperature (e.g., highest, lowest, etc.) ofthe accelerometer 110 that occurred while the calibrated values weredetermined. The monitoring module 360 monitors subsequent temperaturemeasurements from the temperature sensor 125, and if a temperaturemeasurement deviates by more than a temperature threshold (e.g., ±5degrees C.), causes the electronic device 100 to re-calibrate theaccelerometer 110.

In some embodiments, once the calibrated values of the calibrationparameters are determined, the monitoring module 360 may associate acalibration date with the set of calibration values. The calibrationdate is the date/time at which the calibrated values were determined.The monitoring module 360 compares the current date/time with thecalibration time, and if a threshold time (e.g., a day, week, etc.) haselapsed since the calibration time, causes the electronic device 100 tore-calibrate the accelerometer 110.

In some embodiments, once the calibrated values of the calibrationparameters are determined, the monitoring module 360 may start trackinga number of power cycles since the set of calibration values weredetermined. The monitoring module 360 compares a current number of powercycles with a threshold number (e.g., 5, 10, some other number, etc.),and if the current number of power cycles equals the threshold number,causes the electronic device 100 to re-calibrate the accelerometer 110.

FIG. 4 is a flowchart illustrating a process 400 of performing real-timeaccelerometer calibration according to one embodiment. The process ofFIG. 4 is performed by the electronic device 100. Likewise, embodimentsmay include different and/or additional steps, or perform the steps indifferent orders.

The electronic device 100 determines 410 that a threshold number ofacceleration measurements are in a data set. The data set holds amaximum of ‘N’ acceleration measurements, and ‘n’ is the number ofactual acceleration measurements in the data set. For example a data setmay include 128 spaces for acceleration measurements. The thresholdnumber is a number of spaces in the data set that should be filled inorder to ensure that the process is able to determine a solution foreach of the calibration parameters. Additional details regarding how thedata set is populated with acceleration measurements is described belowwith regard to FIG. 5.

The electronic device 100 sets 410 each of the calibration parameters inan accelerometer error correction model (“error correction model”) totheir respective default values. The error correction model may be, forexample, equation (2). The error correction model includes values forbias error calibration parameters, sensitivity calibration parameters,and cross-axis calibration parameters. For example, the electronicdevice 100 may set the values of the bias error calibration parametersand the cross-axis calibration parameters to ‘0’ and the values of thesensitivity calibration parameters to ‘1.’

The electronic device 100 determines 415 values for the bias errorcalibration parameters using the error correction model and the dataset. The electronic device 100 selects a particular bias errorcalibration parameter (e.g., Bx) and fixes the remaining calibrationparameters. The electronic device 100 perturbs the selected bias errorcalibration parameter by a value of A. Specifically, the electronicdevice 100 selects 3 separate values for the selected calibrationparameter which correspond to a most recent value (MRV₀), a most recentvalue −Δ (MRV_(−Δ)), and a most recent value +Δ (MRV_(+Δ)), where Δ isconstant value at a first resolution (e.g., 0.1 millig). The electronicdevice 100 determines an estimated acceleration vector for each of theacceleration measurements in the data set using a MRV_(−Δ) of theparticular bias error calibration parameter, a MRV₀ of the particularbias error calibration parameter, and a MRV_(+Δ) of the particular biaserror calibration parameter, respectively, to generate three estimatedacceleration matrices, Â_(−Δ), Â₀, and Â_(+Δ). For example, Â₀ is shownbelow,

$\begin{matrix}{{\hat{A}}_{0} = \begin{bmatrix}a_{x\; 1}^{\hat{}} & a_{y\; 1}^{\hat{}} & a_{z\; 1}^{\hat{}} \\\vdots & \vdots & \vdots \\a_{x\; n}^{\hat{}} & a_{y\; n}^{\hat{}} & a_{z\; n}^{\hat{}}\end{bmatrix}} & (9)\end{matrix}$

All of the estimated acceleration matrices have the same number of rows(i.e., ‘n’ the number of acceleration measurements in the data set) andcolumns.

The electronic device 100 determines a modified variance for each of thethree estimated acceleration matrices, Â_(−Δ), Â₀, and Â_(+Δ). Forexample, a modified variance, σ, of an estimated acceleration matrix maybe found using equation (3). The electronic device 100 then selects thevalue of the bias error calibration parameter that results in the lowestmodified variance, and sets the selected value as a new MRV₀. Forexample, if the modified variances of the set of row vectors of Â_(−Δ),Â₀, and Â_(+Δ) are 0.3, 0.2, and 0.01, respectively, the electronicdevice 100 selects the MRV_(+Δ) of the bias error calibration parameter,and then sets a new value of MRV₀ as being the value of MRV_(+Δ) becausethe corresponding estimated acceleration matrix, Â_(+Δ), resulted in thelowest modified variance value. The electronic device 100 then selectsnew values for MRV_(+Δ) and MRV_(+Δ). based on the value of the newMRV₀. The electronic device 100 then calculates the accelerationmatrices, calculates modified variances of each estimated accelerationmatrix, and identifies which of the MRV_(−Δ), MRV₀, or MRV_(+Δ), resultsin the lowest modified variance.

This iterative process of adjusting the MRV₀ of the selected bias errorcalibration parameter continues until the MRV₀ (and not the MRV_(−Δ) orthe MRV_(+Δ)) for the particular bias error calibration parameterresults in a corresponding minimum modified variance value. Theelectronic device 100 then reduces the value of Δ by X % (e.g., 50% orsome other value). The electronic device 100 then repeats the abovedescribed iteration for the particular bias error calibration parameter(e.g., Bx) using the new value of Δ until the MRV₀ for the particularbias error calibration parameter results in the minimum modifiedvariance value, and not the MRV_(−Δ) or the MRV_(+Δ). The value of A maybe reduced again, and the above process repeated, until the lowestcalculated modified variance value of the estimated accelerationmatrices is less than or equal to a bias error calibration threshold(e.g., 0.1 millig). The bias error calibration threshold may be, e.g., anumber set by an administrator, or a number set by the bit resolution ofthe electronic device 100. An intermediate value is a value of acalibration parameter that results in a lowest modified variance of anacceleration matrix for a given iteration. Once the bias errorcalibration threshold is reached, the electronic device 100 sets theparticular bias error calibration parameter (e.g., Bx) as theintermediate value.

The electronic device 100 then selects a different bias errorcalibration parameter (e.g., By or Bz) for perturbation. The electronicdevice 100 repeats the above process for the newly selected bias errorcalibration parameter (e.g., By) to identify a correspondingintermediate value. Once complete, the electronic device 100 sets avalue of the different bias error calibration parameter (e.g., By) tothe corresponding intermediate value, and then selects a remaining biaserror calibration parameter (e.g., Bz) for perturbation. The electronicdevice 100 repeats the above process for the last remaining errorcalibration parameter (e.g., Bz) to identify a correspondingintermediate value. The electronic device 100 continues to cycle througheach of the bias error calibration parameters until, for all threecalibration parameters, the most recent values (MRV₀) of the calibrationparameters result in minimum modified variance values that are less thanor equal to the bias error calibration threshold.

The electronic device 100 determines 420 values for sensitivitycalibration parameters and refines the determined values for the biaserror calibration parameters using the error correction model and thedata set. Step 420 is substantially similar to step 415, except inaddition to the bias error calibration parameters, the sensitivitycalibration parameters are also being perturbed. The electronic device100 iteratively perturbs, in a graduated manner (i.e., progressivelyreducing the size of Δ and/or γ), each value of the sensitivitycalibration parameters and the determined values of bias errorcalibration parameters. For example, the electronic device 100sequentially perturbs the 3 sensitivity calibration parameters and the 3bias error calibration parameters. The sensitivity calibrationparameters are perturbed by γ, and the bias error calibration parametersare perturbed by Δ. The electronic device 100 iteratively perturbs thesensitivity calibration parameters and the bias error calibrationparameters until for all the sensitivity calibration parameters and thebias error calibration parameters the most recent values (MRV₀) of thesensitivity calibration parameters result in minimum modified variancevalues that are less than or equal to a sensitivity error threshold andthe most recent values (MRV₀) of the bias error calibration parametersresult in minimum modified variance values that are less than or equalto the bias error threshold.

The electronic device 100 determines 425 calibration values for allcalibration parameters (including cross-axis error) using the errorcorrection model and the data set. Step 425 is substantially similar tosteps 420 and 415, except in addition to the bias error calibrationparameters and the sensitivity calibration parameters, the cross-axiserror calibration parameters are also being perturbed. For example, theelectronic device 100 sequentially perturbs the 6 cross axis errorcalibration parameters, the 3 sensitivity calibration parameters, andthe 3 bias error calibration parameters. The values of the sensitivitycalibration parameters and the bias error calibration parameters arerefined, via continued perturbation, to account for possible changes inthe minimization of the modified variances due to changes in the valuesof the cross-axis error calibration parameters.

The values of the cross-axis error calibration parameters are perturbedby Γ, the sensitivity calibration parameters are perturbed by γ, and thebias error calibration parameters are perturbed by Δ. The electronicdevice 100 iteratively perturbs, in a graduated manner (i.e.,progressively reducing the size of Δ, γ, and/or Γ) each of thecalibration parameters until (1) the most recent values (MRV₀) of eachof the cross-axis error calibration parameters result in minimummodified variance values that are less than or equal to a cross-axiserror calibration threshold; (2) the most recent values (MRV₀) of eachof the sensitivity calibration parameters result in minimum modifiedvariance values that are less than or equal to the sensitivity errorthreshold; and (3) the most recent values (MRV₀) of each of the biaserror calibration parameters result in minimum modified variance valuesthat are less than or equal to the bias error threshold. The values ofthe calibration parameters once (1), (2), and (3) are met are referredto as calibration values for the calibration parameters.

The electronic device 100 receives 430 a new acceleration measurementthat changes the data set. The process 400 is continually receiving newmeasurements, and as discussed in detail below with regard to FIG. 5some of the new acceleration measurements may be used to update theacceleration measurements in the data set. Accordingly, the process flowmoves to step 415, and steps 415, 420, 425, and 430 are looped such thatthe electronic device 100 is always refining the determined calibrationvalues.

The electronic device 100 determines 435 a calibration quality metricusing the determined calibration values. The electronic device 100calculates a calibration quality metric (“C”) using equations (4), (5),(6), and (7).

The electronic device 100 updates the error correction model with thecalibration parameters, and determines calibrated accelerationmeasurements for each of the acceleration measurements in the data setto form a calibrated acceleration matrix. The electronic device 100determines a first metric, m₁, that generally represents how well thecalibrated acceleration measurements in the data set cover a uniformsphere with a 1 g radius. The electronic device 100 identifies a minimumand a maximum value of the x, y, and z components within the calibratedacceleration matrix (will be close to 1 g or −1 g). The electronicdevice 100 then calculates m₁, using for example equation (5). Theelectronic device 100 then determines a variance of the calibratedacceleration matrix, using, for example equation (7). The electronicdevice 100 then calculates a second metric, m₂, using equation (6). Oncem₁ and m₂ are calculated the electronic device 100 calculates C usingequation (4).

The electronic device 100 provides 440 the calibration quality metricand the calibration values to the application 110. For example, theelectronic device 100 may provide the calibration quality metric and thecalibration values to a fitness tracking application operating on theelectronic device 100. In some embodiments, the electronic device 100provides some, but not all of the calibration values to the third partyapplication. For example, the electronic device 100 may provide thecalibration values for the bias error and sensitivity calibrationparameters, but not the cross term error calibration parameters. Inalternate embodiments, the electronic device 100 may provide one or moreof the calibration values, but not the calibration quality metric. Also,in alternate embodiments, the electronic device 100 may provide theerror correction model and/or one or more of the calibration values tothe third party application. In alternate embodiments the electronicdevice 100 updates a register on the accelerometer 110 with values ofthe calibration parameters, which then updates an on-board version ofand/or equation (2) with the determined values for the calibrationparameters.

Once the calibration values are determined, the electronic device 100 isable to determine an estimated acceleration measurement for each newlyreceived acceleration measurement. The received acceleration measurementcorresponds to an estimated acceleration vector that includes an errorcomponent composed of bias error, sensitivity error, cross-axis error,or some combination thereof. The electronic device 100 inputs theacceleration measurement into the updated error correction model to getan estimated acceleration measurement that may be represented as anestimated acceleration vector. The true acceleration vector being offsetfrom the estimated acceleration vector by the error component present inthe estimated acceleration vector. As the calibration becomesprogressively better, the estimated acceleration vector converges to atrue acceleration measurement as the error component converges to somesmall value (e.g., 0.1%). Accordingly, the true acceleration vector maybe approximated by the estimated acceleration vector.

Moreover, as the value of C increases, at some threshold value, theelectronic device 100 may modify one or more of the populationconditions to tighten entry requirements for acceleration measurementsto the data set. For example, the electronic device 100 may reduce themaximum linear acceleration from ±50 millig to ±25 millig.

Additionally, in some embodiments, the electronic device 100 continuallymonitors whether a recalibration parameter is met. If a recalibrationparameter (e.g., elapsed time since previous calibration of theaccelerometer 110) is met, the process 400 moves to step 410 and theaccelerometer 110 is recalibrated.

FIG. 5 is a flowchart illustrating a process 500 of populating a dataset according to one embodiment. The process of FIG. 5 is performed bythe electronic device 100. Likewise, embodiments may include differentand/or additional steps, or perform the steps in different orders.

Initially, the data set includes zero acceleration measurements, and maycontain a total of N acceleration measurements. For example a data setmay include 128 spaces for acceleration measurements.

The electronic device 100 adds 505 an acceleration measurement to a dataset in accordance with population conditions. The population conditionscontrol whether or not the acceleration measurement is added to the dataset. The population conditions include a maximum linear acceleration(e.g., between ±50 millig) within a specified period of time and aminimum threshold angle between the received acceleration measurementand any of the acceleration measurements already present in the dataset. In alternate embodiments, the population conditions mayadditionally include, some other property of an accelerationmeasurement, the number of acceleration measurements in the data set, orsome combination thereof.

Once a new acceleration measurement is received, the electronic device100 determines whether the population conditions are met. For example,as noted above, an acceleration measurement may be broken into agravitational acceleration component, a liner acceleration component,and an angular acceleration component. As the angular accelerationcomponent is generally very small it may be neglected, as thegravitational component is known the electronic device 100 is able todetermine the linear acceleration of the received accelerationmeasurement. Moreover, the electronic device 100 determines how long thelinear acceleration is within the maximum allowed value (e.g., between±50 millig) by comparing the linear acceleration component to linearacceleration components determined from one or more previously receivedacceleration measurements.

As mentioned above, another population condition is that there is atleast a minimum threshold angle (e.g., 7.5 degrees) between the receivedacceleration measurement and the acceleration measurements alreadypresent in the data set, the electronic device 100. For example, theelectronic device 100 uses a dot product based algorithm (e.g., as inequation (1)) to determine that the received acceleration measurement isat least the minimum threshold angle between each of the accelerationmeasurements already in the data set. For example, the electronic device100 may use equation (1) to determine a set of angles between a newacceleration measurement, AM_(new), and each of the accelerationmeasurements in the data set, [AM₁ . . . AM_(N)]. The electronic device100 identifies a minimum angle in the set of angles, and if the minimumangle is greater than the threshold angle value, the populationcondition is met. If the minimum angle is less than the threshold anglevalue, the population condition is not met and AM_(new) is not added tothe data set—even though it may have satisfied other populationconditions. Once the electronic device 100 has determined that all ofthe population conditions are met, the received acceleration measurementis added to the data set.

The electronic device 100 then determines 510 whether the data set isfull. The data set is full if there are no spaces left in the data set.For example, the electronic device 100 determines whether there are Nspaces filled in the data set. If the data set still has empty spaces,the process flow moves to step 505 and the electronic device 100populates the data set in accordance with the population conditionsuntil the data set is full. Once the electronic device 100 determines510 that the data set is full the process flow moves to step 515.

The electronic device 100 receives 515 a new acceleration measurement.In this context, the new acceleration measurement is an accelerationmeasurement that is received after the data set is full. Steps 520-550determine how the electronic device 100 processes the new accelerationmeasurement.

The electronic device 100 determines 520 whether there are any extremumin the data set. The electronic device 100 uses the error correctionmodel to generate an estimated acceleration measurement for each ofacceleration measurements (“a_(existing)”) in the data set. Theestimated acceleration measurements of the existing accelerationmeasurements in the data set all should have a magnitude relativelyclose to an expected value (e.g., 1 g). The electronic device 100determines a magnitude for each of the existing accelerationmeasurements, and identifies an a_(existing) having the maximummagnitude (“Max”) and an a_(existing) having the minimum magnitude(“Min”). The electronic device 100 determines (1) whether the Max valueis below a maximum threshold value, and determines (2) whether the Minvalue is greater than a minimum threshold value. If (1) and (2) aresatisfied, the process flow moves to step 540. In contrast, if (1)and/or (2) are not satisfied the process flow moves to step 525.

In step 525, the electronic device 100 determines 525 whether the newacceleration measurement is closer to the expected value than theextremum. For example, the electronic device 100 uses the errorcorrection model to generate an estimated acceleration measurement forthe new acceleration measurement (“a_(new)”). The electronic device 100determines a magnitude of a_(new), and if the determined magnitude isgreater than or equal to Max or less than or equal to Min, the newmeasurement is not closer to the expected value than the extremum andthe process flow moves to step 530. At step 530, the electronic device100 discards 530 the new acceleration measurement and the process flowmoves to step 515.

In contrast, if the determined magnitude is less than Max or greaterthan Min, the new acceleration measurement is closer to the expectedvalue, and the process moves to step 535. At step 535 the electronicdevice 100 replaces 535 an existing acceleration measurement in the dataset corresponding to the extremum with the new acceleration measurement,and the process flow moves to step 515.

Once the electronic device 100 determines 520 that there are no extremumin the data set, the electronic device 100 identifies 540 twoacceleration measurements that are closest to each other in angle withinthe data set (also referred to as “two closest accelerationmeasurements”). The two closest acceleration measurements include atleast acceleration measurement from the data set, and may include thenew acceleration measurement. In some embodiments, the electronic device100 uses a dot product based algorithm (e.g., as in equation (1)) todetermine an angle between each and every acceleration measurements inthe data set and each and every acceleration measurements in the dataset and the new acceleration measurement. In other embodiments, theelectronic device 100 may use other, possibly more efficient, but morecomplex algorithms to identify the two closest accelerationmeasurements. For example, the electronic device 100 may use a binarysearch algorithm, a nearest neighbor algorithm, or some other algorithmto determine the two closest acceleration measurements that are closestin angle.

The electronic device 100 combines 545 the two closest accelerationmeasurements to generate a combined acceleration measurement. In someembodiments, the electronic device 100 combines the two closestacceleration measurements using a weighted sum to generate a combinedacceleration measurement. In some embodiments, the weight of the twoclosest acceleration measurements are equal. Alternatively, as describedabove with regard to FIG. 3, in some embodiments, the electronic device100 may be configured to weight each of the closest accelerationmeasurements based on a respective number of acceleration measurementsthat were previously combined to generate each of the two closestacceleration measurements. For example, if a first accelerationmeasurement was previously generated by a combination of 4 differentacceleration measurement, and the second acceleration measurements isthe new acceleration measurement, the electronic device 100 weights thefirst acceleration more than the second acceleration measurement.

The electronic device 100 updates 550 the data set with the combinedacceleration measurement and the new acceleration measurement. Inembodiments, where the two closest acceleration measurements areexisting acceleration measurements in the data set each of the twoclosest acceleration measurements are associated with a respective spacein the data set. The electronic device 100 replaces one of the twoclosest acceleration measurements with the combined accelerationmeasurement and replaces the other of the two the new accelerationmeasurements with the new acceleration measurement. In the case whereone of the two closest acceleration measurements is the new accelerationmeasurement, the electronic device 100 replaces the existingacceleration measurement in the data set with the combined accelerationmeasurement. The process flow then moves to step 515, and the electronicdevice 100 receives another new acceleration measurement.

Turning now to simulated examples showing convergence for the errorsources, FIG. 6 is an example plot 600 showing bias calibrationconvergence toward reference truth for x, y, and z axis. The plot 600shows three different simulated sources of bias error: source 610,source 620, and source 630. Source 610 corresponds to a simulated 100millig bias error (i.e., 409.6 g/4096), source 620 corresponds to asimulated 0 millig bias error, and source 630 corresponds to a simulated−100 millig bias error (i.e., −409.6 g/4096). In plot 600 it is apparentthat after approximately 1600 samples (i.e., sequential outputs from theaccelerometer 110) the calibration has converged to values close to thevalues of the sources 610, 620, and 630. Note, in this example, the dataset includes 128 acceleration measurements (i.e., N=128).

FIG. 7 is an example plot 700 showing sensitivity calibrationconvergence toward reference truth for x, y, and z axis. The plot 700shows three different simulated sources of sensitivity error, source710, source 720, and source 730. Source 710 corresponds to a simulatedsensitivity of 1.125 (+12.5% error), source 720 corresponds to asimulated sensitivity of 1 (no error), and source 730 corresponds to asimulated sensitivity of 0.91 (−9% error). In plot 700 it is apparentthat after approximately 1600 samples the calibration has converged tovalues close to the values of the sources 710, 720, and 730. Note, inthis example, the data set includes 128 acceleration measurements (i.e.,N=128).

FIG. 8 is an example plot 800 showing calibration in terms of tiltangle. Plot 800 is based on the same data set that was used to generateFIGS. 6 and 7, and accordingly, also includes bias error and sensitivityerror. Uncalibrated the tilt error is approximately 7 degrees, however,once calibration has occurred the tilt error is approximately 0.2degrees. At a sample rate of 100 Hz, this means it takes approximately16 seconds to calibrate the accelerometer 110 for the simulatedconditions.

OTHER CONSIDERATIONS

Some portions of the above description describe the embodiments in termsof algorithmic processes or operations. These algorithmic descriptionsand representations are commonly used by those skilled in the dataprocessing arts to convey the substance of their work effectively toothers skilled in the art. These operations, while describedfunctionally, computationally, or logically, are understood to beimplemented by computer programs comprising instructions for executionby a processor or equivalent electrical circuits, microcode, or thelike. Furthermore, it has also proven convenient at times, to refer tothese arrangements of functional operations as modules, without loss ofgenerality. The described operations and their associated modules may beembodied in software, firmware, hardware, or any combinations thereof.

As used herein any reference to “one embodiment” or “an embodiment”means that a particular element, media feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment. The appearances of the phrase “in oneembodiment” in various places in the specification are not necessarilyall referring to the same embodiment.

Some embodiments may be described using the expression “coupled” and“connected” along with their derivatives. It should be understood thatthese terms are not intended as synonyms for each other. For example,some embodiments may be described using the term “connected” to indicatethat two or more elements are in direct physical or electrical contactwith each other. In another example, some embodiments may be describedusing the term “coupled” to indicate that two or more elements are indirect physical or electrical contact. The term “coupled,” however, mayalso mean that two or more elements are not in direct contact with eachother, but yet still co-operate or interact with each other. Theembodiments are not limited in this context.

As used herein, the terms “comprises,” “comprising,” “includes,”“including,” “has,” “having” or any other variation thereof, areintended to cover a non-exclusive inclusion. For example, a process,method, article, or apparatus that comprises a list of elements is notnecessarily limited to only those elements but may include otherelements not expressly listed or inherent to such process, method,article, or apparatus. Further, unless expressly stated to the contrary,“or” refers to an inclusive or and not to an exclusive or. For example,a condition A or B is satisfied by any one of the following: A is true(or present) and B is false (or not present), A is false (or notpresent) and B is true (or present), and both A and B are true (orpresent).

In addition, use of the “a” or “an” are employed to describe elementsand components of the embodiments herein. This is done merely forconvenience and to give a general sense of the disclosure. Thisdescription should be read to include one or at least one and thesingular also includes the plural unless it is obvious that it is meantotherwise.

Upon reading this disclosure, those of skill in the art will appreciatestill additional alternative structural and functional designs for asystem and a process for real-time calibration of accelerometers. Thus,while particular embodiments and applications have been illustrated anddescribed, it is to be understood that the described subject matter isnot limited to the precise construction and components disclosed hereinand that various modifications, changes and variations which will beapparent to those skilled in the art may be made in the arrangement,operation and details of the method and apparatus disclosed herein.

1. A method for real-time accelerometer calibration on an electronicdevice, the method comprising: receiving from at least one accelerometera plurality of acceleration measurements, each acceleration measurementrepresenting an estimated acceleration vector, wherein each accelerationvector includes an error component that offsets the estimatedacceleration vector from a true acceleration vector due to a combinationof bias errors, sensitivity errors, and a cross-axis errors, and storingthe acceleration measurements in a data set; maintaining anaccelerometer error correction model that includes bias errorcalibration parameters that specify weights for the bias error of theestimated acceleration vector components; determining calibration valuesfor the bias error calibration parameters using the accelerometer errorcorrection model and the plurality of acceleration measurements; anddetermining a calibration corrected estimate of a true accelerationvector that corresponds to a subsequently received accelerationmeasurement using the determined calibration values and the errorcorrection model.
 2. The method of claim 1, wherein the accelerometererror correction model further includes sensitivity calibrationparameters that specify weights for the sensitivity error of theestimated acceleration vector components, the method further comprising:determining calibration values for sensitivity calibration parametersthat specify weight for the sensitivity error, and refining thedetermined calibration values for the bias error calibration parametersusing the accelerometer error correction model and the plurality ofacceleration measurements.
 3. The method of claim 2, wherein theaccelerometer error correction model further includes cross-axis errorcalibration parameters that specify weights for the cross-axis error ofthe estimated acceleration vector components, the method furthercomprising: determining calibration values for the cross-axis errorcalibration parameters, the sensitivity calibration parameters, and thebias error calibration parameters, and refining the determinedcalibration values of the sensitivity calibration parameters and thebias error calibration parameters, using the accelerometer errorcorrection model and the plurality of acceleration measurements.
 4. Themethod of claim 3, further comprises: setting each of the calibrationparameters in the error correction model to their respective defaultvalue.
 5. The method of claim 4, wherein the accelerometer errorcorrection model is represented by the equation:â=S(a−b) where a is an acceleration vector that represents anacceleration measurement in the data set, b is a vector of the biaserror calibration values, S is a matrix including sensitivity errorcalibration values on the matrix diagonals, and cross-term calibrationvalues occupying the non-diagonal terms, and â is the true accelerationvector representing an estimated acceleration measurement that has beencalibrated.
 6. The method of claim 1, wherein collecting the pluralityof acceleration measurements from the accelerometer to populate the dataset, further comprises: populating the data set with accelerationmeasurements that (1) have a threshold separation in angle with otheracceleration measurements already in the data set, and (2) have a linearacceleration component that is below a maximum threshold linearacceleration for a threshold period of time.
 7. The method of claim 1,further comprising: determining, for each of the accelerationmeasurements in the data set, calibrated acceleration measurements usingthe accelerometer error model to form a set of acceleration vectors; anddetermining a calibration quality metric based in part on a set ofacceleration vectors and a value for Earth's gravity.
 8. The method ofclaim 1, further comprising: providing a calibration quality metric thatis based in part on the calibration values and one or more of thecalibration values to a third party application operating on theelectronic device.
 9. The method of claim 1, further comprising:responsive to determining a recalibration parameter is met,recalibrating the accelerometer.
 10. The method of claim 9, wherein therecalibration parameter is selected from a group comprising: a thresholddeviation in temperature of the accelerometer relative to a temperatureof the accelerometer during a previous calibration, an elapsed timesince the previous calibration of the accelerometer, a number of powercycles, and a user input.
 11. An electronic device, the devicecomprising: an accelerometer that outputs acceleration measurementsrepresenting an estimated acceleration vector, wherein each accelerationvector includes an error component that offsets the estimatedacceleration vector from a true acceleration vector due to bias errors,sensitivity errors, and cross-axis errors; a processor configured toexecute modules; and a memory storing the modules, the modulescomprising: a data collection module configured to determine that athreshold number of acceleration measurements are in a data set; amodeling module configured to maintain an accelerometer error correctionmodel that includes bias error calibration parameters that specifyweights for the bias error of the estimated acceleration vectorcomponents; an error module configured to determine calibration valuesfor the bias error calibration parameters using the accelerometer errorcorrection model and the plurality of acceleration measurements; and anapplication interface module configured to determine a calibrationcorrected estimate of a true acceleration vector that corresponds to asubsequently received acceleration measurement using the determinedcalibration values and the error correction model.
 12. The device ofclaim 11, wherein the accelerometer error correction model furtherincludes sensitivity calibration parameters that specify weights for thesensitivity error of the estimated acceleration vector components, andthe error module is further configured to: determine calibration valuesfor sensitivity calibration parameters that specify weight for thesensitivity error, and refine the determined calibration values for thebias error calibration parameters using the accelerometer errorcorrection model and the plurality of acceleration measurements.
 13. Thedevice of claim 12, wherein the accelerometer error correction modelfurther includes cross-axis error calibration parameters that specifyweights for the cross-axis error of the estimated acceleration vectorcomponents, and the error module is further configured to: determinecalibration values for the cross-axis error calibration parameters, thesensitivity calibration parameters, and the bias error calibrationparameters, and refine the determined calibration values of thesensitivity calibration parameters and the bias error calibrationparameters, using the accelerometer error correction model and theplurality of acceleration measurements.
 14. The device of claim 11,wherein the error module is further configured to: set each of thecalibration parameters in the error correction model to their respectivedefault value.
 15. The device of claim 14, wherein the accelerometererror correction model is represented by the equation:â=S(a−b) where a is an acceleration vector that represents anacceleration measurement in the data set, b is a vector of the biaserror calibration values, S is a matrix including sensitivity errorcalibration values on the matrix diagonals, and cross-term calibrationvalues occupying the non-diagonal terms, and â is the true accelerationvector representing an estimated acceleration measurement that has beencalibrated.
 16. The device of claim 11, wherein the data collectionmodule is further configured to: populate the data set with accelerationmeasurements that (1) have a threshold separation in angle with otheracceleration measurements already in the data set, and (2) have a linearacceleration component that is below a maximum threshold linearacceleration for a threshold period of time.
 17. The device of claim 11,wherein the error module is further configured to: determine, for eachof the acceleration measurements in the data set, calibratedacceleration measurements using the accelerometer error model to form aset of acceleration vectors; and determine a calibration quality metricbased in part on the set of acceleration vectors and a value for Earth'sgravity.
 18. The device of claim 17, wherein the application interfacemodule is further configured to: provide a calibration quality metricthat is based in part on the calibration values and one or more of thecalibration values to a third party application operating on theelectronic device.
 19. A method for real-time accelerometer calibrationon an electronic device, the method comprising: collecting a pluralityof acceleration measurements from an accelerometer to populate a dataset, each acceleration measurement representing an estimatedacceleration vector, wherein each acceleration vector includes an errorcomponent that offsets the estimated acceleration vector from a trueacceleration vector due to a combination of bias error, sensitivityerror, and cross-axis error; maintaining an accelerometer errorcorrection model that includes at least one set of calibrationparameters selected from a group consisting of: bias error calibrationparameters, sensitivity calibration parameters, and cross-axiscalibration parameters that each specify respective weights for each ofthe bias error, the sensitivity error, and the cross-axis error of theestimated acceleration vector components; determining calibration valuesfor the at least one set of error calibration parameters using theaccelerometer error correction model and the plurality of accelerationmeasurements; and providing a calibration quality metric that is basedin part on the calibration values and one or more of the calibrationvalues to a third party application operating on the electronic device.20. The method of claim 19, wherein the at least one set of errorcalibration parameters includes the bias error calibration parameters,the sensitivity calibration parameters, and the cross-axis calibrationparameters, the method further comprising: determining values for thebias error calibration parameters using the accelerometer errorcorrection model and the plurality of acceleration measurements;determining values for sensitivity calibration parameters that specifyweight for the sensitivity error, and refining the determined values forthe bias error calibration parameters using the accelerometer errorcorrection model and the plurality of acceleration measurements; anddetermining calibration values for the cross-axis error calibrationparameters, the sensitivity calibration parameters, and the bias errorcalibration parameters, using the determined values of the sensitivitycalibration parameters and the bias error calibration parameters, theaccelerometer error correction model, and the plurality of accelerationmeasurements.